IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the percent of individuals with the IQ's in the following ranges: (Use the Empirical Rule 68-95-99.7)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Understanding IQ Score Distribution Using the Empirical Rule**
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the percent of individuals with IQs in the following ranges:
*Use the Empirical Rule (68-95-99.7)*
1. **Between 70 and 100:**
[ ] %
2. **Within one standard deviation of the mean:**
[ ] %
3. **Above 145:**
[ ] %
4. **Below 100:**
[ ] %
**Explanation of the Empirical Rule:**
The Empirical Rule, also known as the 68-95-99.7 rule, is used to explain the distribution of data in a normal distribution. Here’s a breakdown:
1. **68% of the data** falls within one standard deviation (σ) of the mean (μ). Mathematically, this is between (μ - σ) and (μ + σ).
2. **95% of the data** falls within two standard deviations of the mean. This range is between (μ - 2σ) and (μ + 2σ).
3. **99.7% of the data** falls within three standard deviations of the mean. The range here is (μ - 3σ) to (μ + 3σ).
Given the mean (μ) is 100 and the standard deviation (σ) is 15 for IQ scores, use these concepts to fill in the blanks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71316fb1-8245-4500-b615-2e27467e4912%2F4f45dfcf-cdfc-4135-b2b0-d0da69aee42d%2Fcpkbn0l_processed.jpeg&w=3840&q=75)
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